That's the question posed by Slate.
From the piece...
Kids still read Andersen's oeuvre, but very few pre-Andersen children's stories remain popular. What did children read before the era of Hans Christian Andersen?
Epic poems, religious literature, romances, and Aesop. Scholars argue over when children's literature—that is, books written exclusively for and read exclusively by children—came into existence. But it's largely a debate over definitions. Even in ancient times, certain types of stories were considered appropriate for children. Archaeologists have unearthed a children's version of the labors of Hercules from the third century written in simple language with large, spaced-out text and color pictures of the lions and the mythical hero. Greek and Roman teachers selected passages from Homer or Virgil that were learner-friendly. And there was always Aesop, the (possibly fictitious) freed slave who supposedly composed fables to illustrate a moral or ethical message. He didn't write his works down, and we'll never know whether children were his intended audience. We do know, however, that Aesop's fables were a crucial part of the education of a Greek or Roman child. Such eminent writers as Plato and Aristophanes referenced Aesop, obviously expecting that their audiences would have come across the fables during their formative years.